Matousek, J: Invitation to Discrete Mathematics 2nd Edition by Jiri Matousek (PDF)

Description

This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science. It is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. Thereaders will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals.The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey’s theorem, and combinatorial applications of linear algebra. General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.

User’s Reviews

Editorial Reviews: Review Review from previous edition: “The book is a self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. It is aimed at undergraduate and early graduate students and encourages an active, problem-solving approach to the material. The book treats selected topics in unusual depth and from several points of view.” ―Zentralblatt fur Didaktik der Mathematik”…a far-from-traditional textbook and…a joy to read. The text is lucid and sprinkled with small jokes and background stories.” ―Times Higher Education Supplement, Friday 26th November 1999 About the Author Jiri Matousek received his PhD in Mathematics from the Charles University in Prague in 1990 and is now Professor of Computer Science at Charles University Prague. He has held several visiting positions at universities in the U.S., Germany, Switzerland, Japan, and other countries. Humboldt Research Fellow in 1992 (Free University Berlin). Prize for Young Mathematicians of the 2nd European Congress of Mathematics in Budapest in 1996, speaker at the ICM 1998. Jaroslav Nesetril received his PhD from the Charles University in Prague in 1975 and is now Professor of Mathematics at Charles University Prague. He has held several visiting positions abroad (U.S.A., Canada, Germany). Currently he is the head of the Centre for Theoretical Computer Science (ITI) at Charles University and the director of the international center for Discrete Mathematics, Theoretical Computer Science and Their Applications (DIMATIA).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐”An Invitation to Discrete Mathmatics” is an excellent textbook for college students, advanced high school students, and curious post-grads like myself. The text is engaging and clear, and the content reveals much of the wonderful capabilities of mathematics for a broad variety of sub-disciplines.

⭐I like discrete math so I really liked this book. Good layout. Clear proofs. Provocative exercise questions. It was in good condition.

⭐Book arrived as described and on time.

⭐Worst math textbook for undergrad. No example, no trivial example, the exercises doesnt have solution and very hard to solve. This is textbook should be use for grad level.

⭐reading this book requires some mathematical maturity. proofs are very clear and easy to follow. examples are very intuitive and relevant. great collection of exercises.

⭐I cannot speak for the English version, which seems to be somewhat lacking in quality of translation, but the Czech version is very engaging and I can highly recommend it for any undergraduate student interested in discrete mathematics.

⭐As another student mentioned, this textbook does not contain a single example. Only definition, statement of theorem, and rigorous proof. This book has minimal emphasis on applications and contains poorly written explanation of stated questions.If you are an instructor, please avoid this book for teaching. Students cannot read this textbook and make sense of it. The math department at our university selected this textbook unfortunately.

⭐I had this textbook in my undergraduate Discrete Math course. I have never written an Amazon review but I feel the need to in this case. The reviews I could find deal with the Czech version and are glowing. The English translation is not useful for those who are trying to learn the material for the first time.1. The text uses analogies and metaphors that don’t seem to be translated to English correctly.2. It is organized as if the lecture was transcribed directly into this book. It is not organized for reading.3. Possibly the worst thing about this book is that there are virtually no examples. The authors use formal proofs to explain the material.4. Often the finial pieces of the proofs are “left as an excersize for the reader” (meaning homework at the end of the chapter). Too make matters worse only “hints” are provided at the back of the book and only for selected excersizes.This is not a book to learn from, even with a very good lecturer I found that referring to this book for topics that were already explained was pointless. The school (Univ of CT) agreed dropping this text in favor of another after only one semester of its use.To get through the course I ended up finding “Discrete Mathematics and Its Applications” by Kenneth H. Rosen and I highly recommend it. If you’re forced to use “Invitation to Discrete Mathematics” in a course I’d suggest you buy a copy of Rosen’s text (even an older edition).

⭐An excellent book by the authors. Thanks alot to the seller for delivering the book in less two weeks to my place.

⭐I will teach Discrete Mathematics and this book is a real treasure. It contains most of the standard topics in the more narrow sense of Discrete Mathematics. That is Combinatorics and Graph Theory. All the proofs are really well explained. Enough exercises, examples, and additional explanations help the students to deepen their understanding. It has enough material to teach a 10-week course.

⭐Für mich als Informatik Student war dieses Buch der ideale Begleiter für das Fach Diskrete Mathematik (Vorlesung mit Rechenübung).Das Buch gibt einen guten Einstieg in die Graphentheorie (aber auch andere Themen werden behandelt).Es ist allerdings keineswegs “vollständig” – viele Grundlagen vermisst man komplett, z.B. flow networks.Die eigentliche Stärke des Buchs ist aber ganz eine andere: man lernt, wie man saubere Beweise führt und wie man “mathematisch denkt”.Man muss sich beim Lesen Zeit lassen und auch mit Zettel und Bleistift bewaffnet den ein oder anderen Beweis nochmal nachrechnen.Insgesamt hat mir das Buch geholfen, die Thematik zu verstehen und auch ein gewisses Interesse dafür zu entwickeln.

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⭐Dass das Schreiben einer Rezension seitens Amazon nicht optional ist, stoert mich (zumal ich ja die bestmoegliche Punktzahl vergeben habe).Das Produkt (Buch) verwende ich zum Lesen (was ist das fuer eine seltsame Frage seitens Amazon).

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